Related papers: Perverse Microsheaves

Let G be a reductive connected group over an algebraic closure of a finite field. I define a tensor structure on the category of perverse sheaves on G which are direct sums of unipotent character sheaves in a fixed two-sided cell, in…

Exotic sheaves are certain complexes of coherent sheaves on the cotangent bundle of the flag variety of a reductive group. They are closely related to perverse-coherent sheaves on the nilpotent cone. This expository article includes the…

We show that the inverse Serre functor for the constructible derived category $\mathbf{D}^\mathrm{b}_\mathrm{c}(\mathbb{P}^n)$ is given by the $\mathbb{P}$-twist at the simple perverse sheaf corresponding to the open stratum. Moreover, we…

Let $pi:X\to\Delta$ be a one-parameter degeneration whose central fiber $X_0$ has a single ordinary double point. The nearby- and vanishing-cycle formalism determines a canonical perverse sheaf on $X_0$, obtained from the variation morphism…

In this paper we prove that the category of parity complexes on the flag variety of a complex connected reductive group is a "graded version" of the category of tilting perverse sheaves on the flag variety of the dual group, for any field…

Using the microlocal theory of sheaves, we associate a category to each Weinstein manifold. By constructing a microlocal specialization functor, we show that exact Lagrangians give objects in our category, and that the category is invariant…

We generalise the notions of scalar-valued holomorphic $p$-contact and $s$-symplectic structures introduced recently on compact complex manifolds by the second-named author jointly with H. Kasuya and L. Ugarte to their analogues with values…

Using punctual gluing of $t$-structures, we construct an analogue of S. Morel's weight truncation functors (for certain weight profiles) in the setting of motivic sheaves. As an application we construct a canonical motivic analogue of the…

We give a geometric model for the category of coherent sheaves over the weighted projective line of type $(p,q)$ in terms of an annulus with marked points on its boundary. We establish a bijection between indecomposable sheaves over the…

We discuss some results on parameterized hypersurfaces which follow quickly from results in the category of perverse sheaves

In characteristic zero, Bezrukavnikov has shown that the category of perverse coherent sheaves on the nilpotent cone of a simply connected semisimple algebraic group is quasi-hereditary, and that it is derived-equivalent to the category of…

In recent work, Graham has constructed a variety with a map to the nilpotent cone which is similar in some ways to the Springer resolution. One aspect in which Graham's map differs is that it is not in general an isomorphism over the…

We give the description of the t-structure on the derived category of regular holonomic D-modules corresponding to the trivial t-structure on the derived category of constructible sheaves via Riemann-Hilbert correspondence. We give also the…

We prove an isomorphism for simple perverse sheaves on the affine Grassmannian of a connected reductive algebraic group that is a geometric counterpart (in light of the Finkelberg-Mirkovi\'c conjecture) of the Steinberg tensor product…

Given a tensor triangulated category we investigate the geometry of the Balmer spectrum as a locally ringed space. Specifically we construct functors assigning to every object in the category a corresponding sheaf and a notion of support…

The geometric and algebraic properties of smooth projective varieties with 1-regular structure sheaf are well understood, and the complete classification of these varieties is a classical result. The aim of this paper is to study the next…

We introduce a singular chain intersection homology theory which generalizes that of King and which agrees with the Deligne sheaf intersection homology of Goresky and MacPherson on any topological stratified pseudomanifold, compact or not,…

A topological condition is given, characterizing which closed manifolds in dimensions < 8 (and conjecturally in general) admit symplectic structures. The condition is the existence of a certain fibration-like structure called a hyperpencil.…

In this thesis we show how to use stack theory to glue description of the category of perverse sheaves P(X,S) on a stratified space (X,S). Hence we give new description of P(X,S) when X is locally C^n stratified by the stratification S…

In this article we classify up to isotopy tight contact structures on Seifert manifolds over the torus with one singular fibre.